Exam-style multiple choice and written questions with full markschemes. Check multiple choice answers straight away, or type, photograph or draw a written answer and get it marked.
A pedestrian follows the three sections of the route shown in Figure 1, starting at O and finishing at P.
Distinguish distance travelled from displacement for the walk shown.
Calculate the distance travelled by the pedestrian.
On Figure 1, draw an arrow to represent the pedestrian’s displacement from O to P.
Determine the magnitude and direction of the displacement from O to P. Give the direction as an angle measured north of east.
A block is attached to a fixed support by a stretched horizontal spring and rests on a rough horizontal table. It remains at rest, and no other horizontal forces act on it. Figure 1 gives the block’s mass and the spring’s constant and extension. Use
Calculate the magnitude of the force exerted by the spring on the block.
Determine the minimum coefficient of static friction between the block and the table for the block to remain at rest.
A sled moves horizontally along a level track. A rope pulls the sled through a displacement of with a constant tension of at above the horizontal. A constant friction force of acts opposite to the motion. The sled’s initial speed is Ignore air resistance.
Calculate the work done on the sled by the tension in the rope.
Calculate the work done on the sled by friction.
Determine the work done by the resultant force on the sled over the displacement.
Determine the sled’s speed after it has moved through
Account for the difference between the work done by the rope and the increase in the sled’s kinetic energy.
In a repeat run, the rope is at above the horizontal. The tension, displacement, initial speed and friction force are unchanged. Calculate the work done by the rope and deduce whether the sled’s final speed is greater or smaller than in the first run.
A horizontal turntable rotates about a fixed vertical axis. Its moment of inertia, excluding two identical small masses, is The masses are moved inward by radial forces through the axis. The bearing exerts negligible torque about the vertical axis. Treat the masses as point particles and the arms as having negligible mass.
Figure 1 shows the initial and final positions of the masses.
Determine the angular speed of the turntable after the masses have moved inward.
Explain why the angular momentum of the turntable–masses system about the vertical axis remains constant while the masses move.
In inertial frame a particle moves along the -axis as shown in Figure 1. Inertial frame moves in the -direction at speed relative to The origins of the frames coincide at Take
The Lorentz transformations are
Determine for the particle in frame
For two events on the particle’s motion, use the Lorentz transformations to show that
Use your answers to (a) and (b) to determine to 2 significant figures.
A trolley moves at constant velocity in the direction relative to the ground. Let be the ground frame and the frame of the trolley. The Galilean transformations are and where is the velocity of relative to
Using the transformations for the positions of an object at two different times, show that its velocity measured in is related to its velocity measured in by
A puck moves at relative to the ground while the trolley moves at relative to the ground. Determine the puck’s velocity relative to the trolley, including its direction.
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