Linear Forces (Dynamics) Practice Questions • Nerd Notes

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What we found:

Assume the posts in the two figures are the same and they have a mass of \( 24 \) \( \text{kg} \) and a length \( L \). Both posts are held vertical by cables attached to the ground and making an angle of \( 36.9^\circ \) with the ground and with the pole, respectively. Both posts are pulled by horizontal forces \( F \). The post on the left is hinged at its lower end and the cable is attached at \( 3/5 \) of the post height from the ground. The post on the right rests on a horizontal surface with a static coefficient of friction \( 0.3 \) and the force is applied at \( 3/5 \) of the height from the ground.

If a net force accelerates a \( 4.5 \) \( \text{kg} \) tool at \( 40 \) \( \text{m/s}^2 \), what acceleration would that same net force give to an \( 18 \) \( \text{kg} \) tool?

A sports car of mass \( 450 \) \( \text{kg} \) accelerates from rest to a speed of \( 100 \) \( \text{km/h} \) in a time interval of \( 4.80 \) \( \text{s} \). What is the magnitude of the force that a passenger of mass \( 68.0 \) \( \text{kg} \) experiences during this acceleration?

A block slides down a frictionless plane having an inclination of \( \theta = 15^{\circ} \). The block starts from rest at the top, and the length of the incline is \( 2.00 \) \( \text{m} \).

A hockey puck struck by a hockey stick is given an initial speed \( v_i \) in the positive \( x \)-direction. The coefficient of kinetic friction between the ice and the puck is \( \mu_k \).

A child tosses a ball straight up. She says that the ball is moving away from her hand because the ball feels an upward “force of the throw” as well as the gravitational force.

The manager of a department store is pushing horizontally with a force of magnitude \( 200 \) \( \text{N} \) on a box of shirts. The box is sliding across the horizontal floor with a forward acceleration. Nothing else touches the box. What must be true about the magnitude of the force of kinetic friction acting on the box?

A rifle bullet with a mass of \( 12.0 \) \( \text{g} \) traveling toward the right at \( 260 \) \( \text{m/s} \) strikes a large bag of sand and penetrates to a depth of \( 23.0 \) \( \text{cm} \). Determine the magnitude and direction of the friction force (assumed constant) that acts on the bullet.

An experiment is performed on a puck on a level air-hockey table, where friction is negligible. A constant horizontal force is applied to the puck, and the puck’s acceleration is measured. Now the same puck is transported far into outer space, where both friction and gravity are negligible. The same constant force is applied to the puck (through a spring scale that stretches the same amount), and the puck’s acceleration (relative to the distant stars) is measured. What is the puck’s acceleration in outer space?

A passenger sitting in the rear of a bus claims that she was injured when the driver slammed on the brakes, causing a suitcase to come flying toward her from the front of the bus. If you were the judge in this case, what disposition would you make? Why?

A person holds a ball in her hand.

How does friction help us walk?

At one instant, a \( 17.5 \) \( \text{kg} \) sled is moving over a horizontal surface of snow at \( 3.50 \) \( \text{m/s} \). After \( 8.75 \) \( \text{s} \) has elapsed, the sled stops. Use a momentum approach to find the average friction force acting on the sled while it was moving.

A boy in a wheelchair (total mass \( 47.0 \) \( \text{kg} \)) has speed \( 1.40 \) \( \text{m/s} \) at the crest of a slope \( 2.60 \) \( \text{m} \) high and \( 12.4 \) \( \text{m} \) long. At the bottom of the slope his speed is \( 6.20 \) \( \text{m/s} \). Assume air resistance and rolling resistance can be modeled as a constant friction force of \( 41.0 \) \( \text{N} \). Find the work he did in pushing forward on his wheels during the downhill ride.

A sled of mass \( m \) is given a kick on a frozen pond. The kick imparts to the sled an initial speed of \( 2.00 \) \( \text{m/s} \). The coefficient of kinetic friction between sled and ice is \( 0.100 \). Use energy considerations to find the distance the sled moves before it stops.

A crate of mass \( 10.0 \) \( \text{kg} \) is pulled up a rough incline with an initial speed of \( 1.50 \) \( \text{m/s} \). The pulling force is \( 100 \) \( \text{N} \) parallel to the incline, which makes an angle of \( 20.0^{\circ} \) with the horizontal. The coefficient of kinetic friction is \( 0.400 \), and the crate is pulled \( 5.00 \) \( \text{m} \).

If all forces on an object are balanced, the object

Which of the following statements about gravitational fields is true?

Two spheres with different masses, \( m \) and \( M \), are separated by a distance \( d \) between their centers. If the gravitational field strength due to the sphere of mass \( M \) at the position of the center of the sphere with mass \( m \) is \( X \), what is the field strength due to the sphere of mass \( m \) at the position of the center of the sphere of mass \( M \)? Select TWO answers.

A block of wood floats in a beaker of water placed inside an elevator. If the elevator begins to accelerate upward at a rate of \( a = \frac{1}{2} g \), how does the volume of the block submerged in the water change?

From what maximum height can a \( 75 \) \( \text{kg} \) person jump without breaking the lower leg bone of either leg? Ignore air resistance and assume the CM of the person moves a distance of \( 0.60 \) \( \text{m} \) from the standing to the seated position (that is, in breaking the fall). Assume the breaking strength (force per unit area) of bone is \( 170 \times 10^{6} \) \( \text{N/m}^2 \), and its smallest cross-sectional area is \( 2.5 \times 10^{-4} \) \( \text{m}^2 \). [Hint: Do not try this experimentally.]

During a Chicago storm, winds can whip horizontally at speeds of \( 100 \) \( \text{km/h} \). If the air strikes a person at the rate of \( 40 \) \( \text{kg/s} \) per square meter and is brought to rest, estimate the force of the wind on a person. Assume the person is \( 1.50 \) \( \text{m} \) high and \( 0.50 \) \( \text{m} \) wide. Compare to the typical maximum force of friction (\( \mu \approx 1.0 \)) between the person and the ground, if the person has a mass of \( 70 \) \( \text{kg} \).

A \( 4.0 \) \( \text{kg} \) block is held in place against a spring with spring constant \( 1100 \) \( \text{N/m} \). The spring is compressed \( 25 \) \( \text{cm} \) from its equilibrium position. After release, the block slides without friction along a track that first contains a vertical circular loop of radius \( 20 \) \( \text{cm} \) and then continues up a straight incline that makes an angle of \( 20^{\circ} \) with the horizontal, as shown in Figure \( 1 \). Assume friction between the block and the track is negligible throughout the motion.

A person stands on a scale in an elevator. If the scale reads \( 600 \) \( \text{N} \) when that person is riding upward at a constant velocity of \( 4 \) \( \text{m/s} \), what is the scale reading when the elevator is at rest?

A \( 100 \) \( \text{N} \) lawnmower is being pushed with a handle that makes a \( 37^\circ \) angle to the ground. There is \( 10 \) \( \text{N} \) of friction between the mower and the ground. What force must be applied to the handle of the mower to get it to accelerate at \( 3 \) \( \text{m/s}^2 \)?

Traveling at a speed of \( 22 \) \( \text{m/s} \), the driver of an automobile suddenly locks the wheels by slamming on the brakes. The coefficient of friction between the tires and the road is \( 0.68 \). How much time does it take for the car to come to a halt? As usual, ignore the effects of air resistance and anything else that could interfere with this problem.

An astronaut with mass \( 75 \) \( \text{kg} \) travels to Mars. Determine his weight under the following conditions.

An elevator carrying a person of mass \( m \) is moving upward and slowing down. How does the magnitude \( F \) of the force exerted on the person by the elevator floor compare with the magnitude \( mg \) of the gravitational force?

A horizontal tension force of \( 8.0 \) \( \text{N} \) is used to pull a \( 20 \) \( \text{N} \) wooden box toward the right along a horizontal wood surface. The coefficient of kinetic friction for wood on wood is \( \mu = 0.3 \).

A \( 52 \) \( \text{N} \) sled is pushed across a cement sidewalk at constant velocity. A horizontal pushing force of \( 36 \) \( \text{N} \) is exerted.

A \( 20 \) \( \text{N} \) force due north and a \( 20 \) \( \text{N} \) force due east act concurrently on an object, as shown in the diagram to the right. What additional force is needed to bring the object into a state of equilibrium?

A force of \( 525 \) \( \text{N} \) is applied to a stationary couch of mass \( 150 \) \( \text{kg} \), where \( \mu_s = 0.33 \) and \( \mu_k = 0.22 \). What is the acceleration of the couch?

Two objects, A and B, move toward one another. Object A has \( 2 \) times the mass and \( \tfrac{1}{2} \) the speed of object B. Which of the following describes the forces the objects exert on each other when they collide and provides the best explanation?

A \( 150 \) \( \text{kg} \) box is pushed horizontally along the floor with a force of \( 650 \) \( \text{N} \). If the coefficient of friction between the box and the floor is \( 0.21 \), calculate its acceleration.

An object is moving to the west at a constant speed. Three forces are exerted on the object. One force is \( 10 \) \( \text{N} \) directed due north, and another is \( 10 \) \( \text{N} \) directed due west. What is the magnitude and direction of the third force if the object is to continue moving to the west at a constant speed?

Does a couch of mass \( 150 \) \( \text{kg} \) move on a carpeted floor with \( \mu_s = 0.33 \) and \( \mu_k = 0.22 \), if it is pushed with a force of \( 400 \) \( \text{N} \)?

A block is initially at rest on top of an inclined ramp that makes an angle \( \theta_0 \) with the horizontal. The distance measured along the base of the ramp is \( D \). After the block is released from rest, it slides down the frictionless ramp and then continues onto a rough horizontal surface until it finally comes to rest at the position \( x = 4D \) measured from the base of the ramp. The coefficient of kinetic friction between the block and the rough horizontal surface is \( \mu_k \).(a) On the axes provided, sketch and label graphs of the following quantities as a function of the position \( x \) of the block for \( -D \le x \le 4D \). Both graphs must use the same vertical scale. i. The kinetic energy \( K \) of the block ii. The gravitational potential energy \( U_g \) of the block–Earth system(b) The block is now released from the top of a different ramp that still makes the same angle \( \theta_0 \) with the horizontal but whose base length is \( 2D \). A student is asked whether the block’s final horizontal position will now be twice as far (i.e., at \( x = 8D \)) compared with the original situation. The student reasons that, because the new height is twice the original height, the block will have more energy at the base of the new ramp and therefore will slide farther along the horizontal surface until stopping at \( x = 8D \). i. Which aspects of the student’s reasoning, if any, are correct? If none are correct, write “none”. ii. Which aspects of the student’s reasoning, if any, are incorrect? If none are incorrect, write “none”.(c) Derive an equation for the new final position of the block in terms of \( D \).(d) Referring to the mathematical relationships you obtained in part (c): • For any correct aspects identified in part (b)(i), explain how your relationships support the student’s reasoning. • For any incorrect aspects identified in part (b)(ii), explain how your relationships correct the student’s reasoning.

A \( 25.0 \) \( \text{kg} \) block is initially at rest on a horizontal surface. A horizontal force of \( 75.0 \) \( \text{N} \) is required to set the block in motion, after which a horizontal force of \( 60.0 \) \( \text{N} \) is required to keep the block moving with constant speed.

Describe two examples in which the force of friction exerted on an object is in the direction of motion of the object.

A traffic light hangs from a pole as shown in the accompanying diagram. The uniform aluminum pole AB is of length \( 7.20 \) \( \text{m} \) and has a mass of \( 12.0 \) \( \text{kg} \). The mass of the traffic light is \( 21.5 \) \( \text{kg} \). The point C is located \( 3.80 \) \( \text{m} \) vertically above the pivot A. A massless horizontal cable CD is attached at C and connects to the pole at point D, where the pole makes an angle of \( 37^{\circ} \) with the cable.

When a box is about to slide but hasn’t moved yet, which friction is acting?

A car is going through a dip in the road whose curvature approximates a circle of radius \( 200 \) \( \text{m} \). At what velocity will the occupants of the car appear to weigh \( 20\% \) more than their normal weight \( (1.2\,W) \)?

The occupants of a car traveling at a speed of \( 30 \) \( \text{m/s} \) note that on a particular part of a road their apparent weight is \( 15\% \) higher than their weight when driving on a flat road.

A car is going over the top of a hill whose curvature approximates a circle of radius \( 350 \) \( \text{m} \). At what velocity will the occupants of the car appear to weigh \( 10\% \) less than their normal weight?

A loop-de-loop roller coaster has a radius of \( 30 \) \( \text{m} \). Determine the apparent weight a \( 500 \) \( \text{N} \) person will feel at the bottom of the loop while traveling at a speed of \( 25 \) \( \text{m/s} \) and at the top of the loop while traveling at a speed of \( 20 \) \( \text{m/s} \).

When a falling meteoroid is at a distance above the Earth’s surface of \( 3.00 \) times the Earth’s radius, what is its acceleration due to the Earth’s gravitation?

Are astronauts really “weightless” while in orbit?

If I weigh \( 741 \) \( \text{N} \) on Earth at a place where \( g = 9.80 \) \( \text{m/s}^2 \) and \( 5320 \) \( \text{N} \) on the surface of another planet, what is the acceleration due to gravity on that planet?

Two balls have their centers \( 2.0 \) \( \text{m} \) apart. One ball has a mass of \( 8.0 \) \( \text{kg} \). The other has a mass of \( 6.0 \) \( \text{kg} \). What is the gravitational force between them?

Two spherical objects have equal masses and experience a gravitational force of \( 25 \) \( \text{N} \) towards one another. Their centers are \( 36 \) \( \text{cm} \) apart. Determine each of their masses.