Reference no: EM132369275
Show all working clearly and include diagrams where appropriate.
1. Calculate the gravitational force between the earth (mass = 6 × 1024 kg ) and the sun (m = 2 × 1030 kg) given that they are 150 000 000 km apart. Use G= 6.67 × 10-11 Nm2kg-2.
2. A runner with a mass of 55 kg, pushes off from the running blocks with a force of 600 N. If this force was exerted over 0.3 s, calculate the speed at which the runner leaves the block.
3. A girl (mass of 50 kg) on rollerskates is travelling in a straight line at 6m s-1 holding a bag of mass 8 kg. She throws the bag directly forward at 12m s-1 relative to the ground. Calculate the girl's velocity immediately after throwing the bag.
4. A pellet launched horizontally drops 45 cm below the object at which it was aimed. If the pellet had an initial velocity of 60 ms-1, what was the horizontal distance to the target? Ignore air resistance.
5. The driver of a 4.2 tonne truck takes his foot off the accelerator and coasts to a stop. If the truck was originally travelling at 28.0 m/s and it takes 320 m to stop.
a. What was the truck's deceleration?
b. What was the frictional force causing the deceleration?
c. What is the coefficient of friction of the road with the wheels?
6. A cyclist takes 15 s to travel around a circular track of radius 50m. Calculate the speed of the cyclist.
7. An object (300 g) is swung in a circle on the end of a 1.2 m length of rope. If the object is travelling at 0.60 ms-1, calculate the tension in the rope.
8. How much work is done if a wheeled toy is pulled 15 m along the ground with a rope as shown in the diagram?
9. A motor pulls a 750 kg roller-coaster to the top of a 50.0 m hill at a constant speed in 75.0 s. What is the power of the motor?
10. A rubber ball is dropped from a height of 2.60 m. If it only bounces to a height of 1.90 m, what percentage of the ball's energy has been dissipated?
11. A ballistic pendulum can be used to measure the speed of bullets. A bullet (mass of 5.0 g) is fired into a block of wood (mass of 4.995 kg) hanging from two cords. The block with the embedded bullet swings up to a maximum vertical height of 7 cm.
Assuming that the kinetic energy of the block at the bottom of the swing is converted to gravitational energy at the top of the swing, calculate:
a. The potential energy at the top of the swing.
b. The velocity of the block plus bullet at the bottom of the swing.
c. The momentum of the block plus bullet at the bottom of the swing.
d. Given that momentum is conserved in the collision of the bullet with the block, calculate the velocity of the bullet just before it strikes the block.
12. Pendulum experiment
The relationship between the period (T), the time for one swing over and back to its original position, and the length (L) of a pendulum is given by the formula:
T = 2Π√L/g where g is the acceleration due to gravity on earth.
The following experiment can be used to calculate a value for g, the acceleration due to gravity.
A pendulum experiment was carried out on earth. A mass, suspended on a string, was held to a set position on one side and then allowed to swing. The time for 10 oscillations was measured and the period for one oscillation calculated. The experiment was repeated for the same mass, the same starting position (θ) but with varying pendulum lengths. Data collected for the pendulum length and the period for one oscillation is shown in the table below.
Table: Pendulum data: Length vs period.
|
Length - L
(m)
|
Period - T
(s)
|
Square of Period - T2 (s2)
|
|
0.05
|
0.46
|
|
|
0.10
|
0.63
|
|
|
0.15
|
0.78
|
|
|
0.20
|
0.93
|
|
|
0.25
|
1.01
|
|
|
0.30
|
1.10
|
|
|
0.35
|
1.19
|
|
|
0.40
|
1.27
|
|
|
0.45
|
1.35
|
|
|
0.50
|
1.42
|
|
|
0.55
|
1.49
|
|
|
0.60
|
1.55
|
|
|
0.65
|
1.66
|
|
|
0.70
|
1.68
|
|
|
0.75
|
1.72
|
|
a. Complete the table to give values for T2 (Square of the period).
b. Rewrite the equation T = 2Π√L/g to make T2 the subject. (Hint: The equation y = √x can be rewritten as y2 = x.)
c. Plot T2 (square of the period) on the vertical axis against L (length of the pendulum) on the horizontal axis.
d. Draw a line of best fit and calculate the gradient.
e. Using the gradient of the line of best fit, calculate a value for g- the acceleration due to gravity on earth. (Hint: Refer back to Module 1: Section 1.4.5).