An object of mass 1 kg is thrown downwards from a height of 20 m . The initial speed of the object is .
The object hits the ground at a speed of . Assume . What is the best estimate of the energy transferred from the object to the air as it falls?
A motor of input power 160 W raises a mass of 8.0 kg vertically at a constant speed of . What is the efficiency of the system?
A student strikes a tennis ball that is initially at rest so that it leaves the racquet at a speed of . The ball has a mass of kg and the contact between the ball and the racquet lasts for ms.
Calculate the average force exerted by the racquet on the ball.
Calculate the average power delivered to the ball during the impact.
Show that the tennis ball passes over the net.
The student strikes the tennis ball at point P. The tennis ball is initially directed at an angle of 7.00° to the horizontal.
Height of P = 2.80 m Distance of student from net = 11.9 m Height of net = 0.910 m Initial speed of tennis ball = 64 m s^(-1)
Calculate the time it takes the tennis ball to reach the net.
Determine the speed of the tennis ball as it strikes the ground.
The student models the bounce of the tennis ball to predict the angle θ at which the ball leaves a surface of clay and a surface of grass.
The model assumes
Predict for the student's model, without calculation, whether θ is greater for a clay surface or for a grass surface.
This question is about the motion of a bicycle. A cyclist is moving up a slope that is at an angle of 19° to the horizontal. The mass of the cyclist and the bicycle is 85 kg.
Calculate the component of the weight of the cyclist and bicycle parallel to the slope.
Calculate the normal reaction force on the bicycle from the slope.
At the bottom of the slope the cyclist has a speed of 5.5 m s⁻¹. The cyclist stops pedalling and applies the brakes which provide an additional decelerating force of 250 N. Determine the distance taken for the cyclist to stop. Assume air resistance is negligible and that there are no other frictional forces.
The diagram shows the trajectory of a projectile and the velocity of the projectile at point in its trajectory. P is located before the projectile reaches the peak altitude. Air resistance acts on the projectile. The acceleration of the projectile at P is a.
What are the magnitudes of the horizontal component and the vertical component of the acceleration of the projectile at P ?
Horizontal component of | Vertical component of | |
---|---|---|
A. | zero | greater than |
B. | non-zero | greater than |
C. | zero | |
D. | non-zero |
A small metal pendulum bob is suspended at rest from a fixed point with a length of thread of negligible mass. Air resistance is negligible. The pendulum begins to oscillate. Assume that the motion of the system is simple harmonic, and in one vertical plane. The graph shows the variation of kinetic energy of the pendulum bob with time.
When the 75 g bob is moving horizontally at 0.80 m/s, it collides with a small stationary object also of mass 75 g. The object and the bob stick together.
Calculate, in m, the length of the thread. State your answer to an appropriate number of significant figures.
Label on the graph with the letter X a point where the speed of the pendulum is half that of its initial speed.
The mass of the pendulum bob is 75 g. Show that the maximum speed of the bob is about 0.7 m/s–1.
Calculate the speed of the combined masses immediately after the collision.
Show that the collision is inelastic.
Sketch, on the axes, a graph to show the variation of gravitational potential energy with time for the bob and the object after the collision. The data from the graph used in (a) is shown as a dashed line for reference.
The speed after the collision of the bob and the object was measured using a sensor. This sensor emits a sound of frequency and this sound is reflected from the moving bob. The sound is then detected by the sensor as frequency .
Explain why and are different.
An object is projected vertically upwards at time t = 0. Air resistance is negligible. The object passes the same point above its starting position at times 2s and 8s.
If g = 10 m s, what is the initial speed of the object?
A projectile is fired from level ground with speed at an angle to the ground. Ignoring air resistance, which of the following is a correct expression for the maximum height reached by the projectile?
A projectile is fired horizontally from the top of a cliff. The projectile hits the ground 4 s later at a distance of 2 km from the base of the cliff. What is the height of the cliff?
A stone is thrown at an angle to the horizontal. Ignoring air resistance, the horizontal component of the initial velocity of the stone determines the value of