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An object undergoes constant acceleration. Starting from rest, the object travels \( 5 \, \text{m} \) in the first second. Then it travels \( 15 \, \text{m} \) in the next second. What additional distance will be covered in the third second?
What is a man’s apparent weight at the equator if his weight is \(500 \, \text{N}\)? The Earth’s radius is \(6.37 \times 10^{6} \, \text{m}\).
Consider a rigid body that is rotating. Which of the following is an accurate statement?
Which of the following must be true for an object at translational equilibrium?
The diagram above shows a marble rolling down an incline, the bottom part of which has been bent into a loop. The marble is released from point A at a height of \(0.80 \, \text{m}\) above the ground. Point B is the lowest point and point C the highest point of the loop. The diameter of the loop is \(0.35 \, \text{m}\). The mass of the marble is \(0.050 \, \text{kg}\). Friction forces and any gain in kinetic energy due to the rotating of the marble can be ignored. When answering the following questions, consider the marble when it is at point C.
A grinding wheel is in the form of a uniform solid disk of radius \( 7.00 \) \( \text{cm} \) and mass \( 2.00 \) \( \text{kg} \). It starts from rest and accelerates uniformly under the action of the constant torque of \( 0.600 \) \( \text{N m} \) that the motor exerts on the wheel.
A boulder is raised above the ground so that its potential energy is \(550 \, \text{J}\). Then it is dropped. Assuming \(92 \, \text{J}\) of energy was lost to air resistance, what is the kinetic energy of the boulder just before it hits the ground?
Given the graph of velocity versus time for a duck flying due south for the winter, at what labeled point did the duck stop its forward motion?
A bowling ball moving with speed \(v\) collides head-on with a stationary tennis ball. The collision is elastic and there is no friction. The bowling ball barely slows down. What is the speed of the tennis ball after the collision?
A constant force of strength \( 20 \) \( \text{N} \) acts on an object of mass \( 3 \) \( \text{kg} \) as it moves a distance of \( 4 \) \( \text{m} \). If this force is applied perpendicular to the \( 4 \) \( \text{m} \) displacement, the work done by the force is equal to:
Two people, one of mass \( 88 \) \( \text{kg} \) and the other of mass \( 55 \) \( \text{kg} \), sit in a rowboat of mass \( 70 \) \( \text{kg} \). With the boat initially at rest, the two people, who have been sitting at opposite ends of the boat \( 3.1 \) \( \text{m} \) apart from each other, now exchange seats.
A space probe far from the Earth is travelling at \( 14.8 \) \( \text{km s}^{-1} \). It has mass \( 1\,312 \) \( \text{kg} \). The probe fires its rockets to give a constant thrust of \( 156 \) \( \text{kN} \) for \( 220. \) \( \text{s} \). It accelerates in the same direction as its initial velocity. In this time it burns \( 150. \) \( \text{kg} \) of fuel.
Calculate the final speed of the space probe in \( \text{km s}^{-1} \).
A miniature, solid globe with mass \( 0.25 \) \( \text{kg} \) and radius \( 0.10 \) \( \text{m} \) is spinning in place about a vertical axis with the equator horizontal, as shown. A point on the globe’s equator, represented by the dot in the figure, has a linear speed of \( 4.0 \) \( \text{m/s} \). The rotational inertia of a solid sphere of mass \( m \) and radius \( r \) is \( \tfrac{2}{5}mr^{2} \). The rotational kinetic energy of the globe is most nearly
Ben’s favorite ride at the Barrel-O-Fun Amusement Park is the Flying Umbrella, which is lifted by a hydraulic jack. The operator activates the ride by applying a force of \( 72 \) \( \text{N} \) to a \( 3.0 \) \( \text{cm} \) wide cylindrical piston, which holds the \( 20,000 \) \( \text{N} \) ride off the ground. What is the diameter of the piston that holds the ride?
A \(20 \, \text{g}\) piece of clay moving at a speed of \(50 \, \text{m/s}\) strikes a \(500 \, \text{g}\) pendulum bob at rest. The length of a string is \(0.8 \, \text{m}\). After the collision, the clay-bob system starts to oscillate as a simple pendulum.
When a horizontal force of \( 4.5 \, \text{N} \) acts on a block on a resistance-free surface, it produces an acceleration of \( 2.5 \, \text{m/s}^2 \). Suppose a second \( 4.0 \, \text{kg} \) block is dropped onto the first. What is the magnitude of the acceleration of the combination if the same force continues to act? Assume that the second block does not slide on the first block.
A force \(F\) is used to hold a block of mass \(m\) on an incline as shown in the diagram above. The plane makes an angle of \(\theta\) with the horizontal and \(F\) is perpendicular to the plane. The coefficient of friction between the plane and the block is \(\mu\). What is the minimum force \(F\) necessary to keep the block at rest?
In 2014, the European Space Agency placed a satellite in orbit around comet 67P/Churyumov-Gerasimenko and then landed a probe on the surface. The actual orbit was elliptical, but we can approximate it as a 50 km diameter circular orbit with a period of 11 days.
A 1100 kg car accelerates from 32 m/s to 8.0 m/s in 4.0 sec. What amount of force was needed to slow it down?
Late one morning, a mosquito collides with the windshield of a speeding truck. The force of the truck on the mosquito is ____ the force of the mosquito on the truck; the resulting acceleration of the mosquito is ____ the acceleration of the truck.
How does the time t1 of a block m reaching the bottom of slide 1 compare with t2, the time taken block of mass 2m to reach the end of slide 2 that’s curved? The blocks are released from the same height.
A proton (mp = 1.67 x10-27 kg) is being accelerated along a straight line at 3.6 ×1015 m/s2 in a machine. The proton has an initial speed of 2.4 x107 m/s and travels 3.5 cm.
A projectile is launched at \( 25 \) \( \text{m/s} \) at an angle of \( 45^\circ \). It lands on a slope \( 5 \) \( \text{m} \) below the launch height. On landing, it rebounds vertically with \( 80\% \) of its speed and falls straight down from there. Find the total time from launch to final impact at the base of the slope.
Determine the sum of the three vectors given below. Calculate the resultant \( \vec{R} \) expressed as:
(a) Vector components
(b) Resultant vector (its total magnitude and direction)
\[\vec{A} = 26.5 \, \text{m} \ @ \ 56^\circ \, \text{NW}\]
\[\vec{B} = 44 \, \text{m} \ @ \ 28^\circ \, \text{NE}\]
\[\vec{C} = 31 \, \text{m} \, \text{South}\]
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