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In which of the following cases does a car have a negative velocity and a positive acceleration? A car that is traveling in the:
A block of mass \( 4.0 \) \( \text{kg} \) rests on an inclined plane. The coefficient of static friction between the block and the plane \( \mu_s \) is \( 0.4 \). Which of the following gives the angle of inclination at which the block will start to slide?
A mechanic pushes a \(2500 \, \text{kg}\) car from rest to a final speed \(v\) by doing \(5.0 \times 10^3 \, \text{J}\) of work on the car. Frictional effect between the car and the ground are negligible. What is the final speed of the car?
A car is traveling \(20 \, \text{m/s}\) when the driver sees a child standing on the road. She takes \(0.8 \, \text{s}\) to react then steps on the brakes and slows at \(7.0 \, \text{m/s}^2\). How far does the car go before it stops?
Divers in Acapulco jump from a cliff that is \( 36 \, \text{m} \) above the water with an initial vertical velocity of \( 2 \, \text{m/s} \).
A 1.0-kg object is moving with a velocity of 6.0 m/s to the right. It collides and sticks to a 2.0-kg object moving with a velocity of 3.0 m/s in the same direction. How much kinetic energy was lost in the collision?
A block sliding down an frictionless inclined plane is experiencing both gravitational and normal forces; which force’s magnitude changes when the angle of the incline is increased?
A vehicle is moving at a speed of 12.3 m/s on a decline when the brakes of all four wheels are fully applied, causing them to lock. The slope of the decline forms an angle of 18.0 degrees with the horizontal plane. Given that the coefficient of kinetic friction between the tires and the road surface is 0.650.
A rocket is fired at a speed of \(75.0 \, \text{m/s}\) from ground level, at an angle of \(60.0^\circ\) above the horizontal. The rocket is fired toward an \(11.0 \, \text{m}\)-high wall, which is located \(27.0 \, \text{m}\) away. The rocket attains its launch speed in a negligibly short period of time, after which its engines shut down and the rocket coasts. By how much does the rocket clear the top of the wall?
Two blocks made of different materials, connected by a thin cord, slide down a plane ramp inclined at an angle \( \theta = 32^\circ \) above the horizontal. If the coefficients of friction are \( \mu_A = 0.2 \) and \( \mu_B = 0.3 \) and if \( m_A = m_B = 5.0 \) \( \text{kg} \), determine:
Two racing boats set out from the same dock and speed away at the same constant speed of \(101 \, \text{km/h}\) for half an hour (\(0.5 \, \text{hr}\)). Boat 1 is headed \(27.6^\circ\) south of west, and Boat 2 is headed \(35.3^\circ\) south of west, as shown in the graph above. During this half-hour calculate:
Two identical spheres are held under water. Sphere A is made of aluminum (density \( 2700 \) \( \text{kg/m}^3 \)) and Sphere B is made of lead (density \( 11300 \) \( \text{kg/m}^3 \)). When both are released and remain fully submerged, how do the buoyant forces \( F_{BA} \) and \( F_{BB} \) compare?
In the context of fluid dynamics, what does the term ‘mass flow rate’ represent in the continuity equation?
A wheel of moment of inertia of \( 5.00 \) \( \text{kg} \cdot \text{m}^2 \) starts from rest and accelerates under a constant torque of \( 3.00 \) \( \text{N} \cdot \text{m} \) for \( 8.0 \) \( \text{s} \). What is the wheel’s rotational kinetic energy at the end of \( 8.0 \) \( \text{s} \)?
The alarm at a fire station rings and a 79.34-kg fireman, starting from rest, slides down a pole to the floor below (a distance of 4.20 m). Just before landing, his speed is 1.36 m/s. What is the magnitude of the kinetic frictional force exerted on the fireman as he slides down the pole?
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 \(3800 \, \text{kg}\) open railroad car coasts along with a constant speed of \(8.60 \, \text{m/s}\) along a level track. Snow begins to fall vertically and fills the car at a rate of \(3.50 \, \text{kg/min}\). Ignoring friction with the tracks, what is the speed of the car after \(90 \, \text{min}\)?
A spacecraft accelerates at a rate of \(20.0 \, \text{m/s}^2\).
A toy car moves off the edge of a table that is \(1.25 \, \text{m}\) high. If the car lands \(0.40 \,\text{m}\) from the base of the table…
Three students are pulling on a bag of skittles. Each applies a horizontal force. Student \( 1 \) pulls eastward with a force of \( 170 \) \( \text{N} \). Student \( 2 \) pulls southward with a force of \( 100 \) \( \text{N} \). Student \( 3 \) pulls with a force of \( 200 \) \( \text{N} \) at an angle of \( 20^{\circ} \) west of north. What is the net force exerted on the bag of skittles by the three students?
A point \( P \) is subjected to three simultaneous forces of magnitudes \( F_A > F_B > F_C \). Point \( P \) is in equilibrium. Which of the following statements is not always true about the magnitudes of the forces?
A car moving at 30 m/s makes a head-on collision with a stone wall. From what height would the car have to fall in order to make an equally hard collision with the ground?
Which of the following best describes ‘gauge pressure’ at a certain depth in a static fluid?
There are two cables that lift an elevator, each with a force of \(10{,}000 \, \text{N}\). The \(1{,}000 \, \text{kg}\) elevator is lifted from the first floor and accelerates over \(10 \, \text{m}\) until it reaches its top speed of \(6 \, \text{m/s}\). What is the mass of the people in the elevator?
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