The table below shows the speed of a marble with time as it rolls along the floor. Use the
given box below to answer the following task.
Speed (m/s) 35 30 25 20 15
Time (s) 0 1 2 3 4
a. Plot a speed time-graph.
b. Calculate the acceleration of the marble
c. Determine the distance travelled.
Answers
Answer:
equation ΔPEg = mgh applies for any path that has a change in height of h, not just when the mass is lifted straight up. (See Figure 2.) It is much easier to calculate mgh (a simple multiplication) than it is to calculate the work done along a complicated path. The idea of gravitational potential energy has the double advantage that it is very broadly applicable and it makes calculations easier.
From now on, we will consider that any change in vertical position h of a mass m is accompanied by a change in gravitational potential energy mgh, and we will avoid the equivalent but more difficult task of calculating work done by or against the gravitational force.
ΔPEg = mgh for any path between the two points. Gravity is one of a small class of forces where the work done by or against the force depends only on the starting and ending points, not on the path between them.
EXAMPLE 1. THE FORCE TO STOP FALLING
A 60.0-kg person jumps onto the floor from a height of 3.00 m. If he lands stiffly (with his knee joints compressing by 0.500 cm), calculate the force on the knee joints.
Strategy
This person’s energy is brought to zero in this situation by the work done on him by the floor as he stops. The initial PEg is transformed into KE as he falls. The work done by the floor reduces this kinetic energy to zero.
Solution
The work done on the person by the floor as he stops is given by W = Fd cos θ = −Fd, with a minus sign because the displacement while stopping and the force from floor are in opposite directions (cos θ = cos 180º = −1). The floor removes energy from the system, so it does negative work.
The kinetic energy the person has upon reaching the floor is the amount of potential energy lost by falling through height h: KE = −ΔPEg = −mgh.
The distance d that the person’s knees bend is much smaller than the height h of the fall, so the additional change in gravitational potential energy during the knee bend is ignored.
The work W done by the floor on the person stops the person and brings the person’s kinetic energy to zero: W = −KE = mgh.
Combining this equation with the expression for W