LAW OF ACCELERATION: SOLVE THE FOLLOWING PROBLEMS:
Use this formula: a = F m
Take Note: Acceleration due to gravity is 9.8 m/s2
A 500 kg car and rider accelerate at 13.5 m/s^2. How much extra force was applied?
What is the acceleration of a 50kg cart if the net force on it is 40N ?
What is the weight of a 80.2 kg person on the surface of the Earth?
A 75.0 kg person weighs 94.0 N on the Moon. What is the acceleration of gravity on the Moon?
50.0 kg Yuri Gagarin is freely floating in space and pushes on a freely floating 85.0 kg spacecraft with a force of 20.0 N for 2 seconds.
Compare the forces exerted by Yuri Gagarin and the spacecraft and,
Compare the acceleration of Yuri Gagarin to the acceleration of the spacecraft.
1. For the first problem, we can use the formula a = F/m to find the extra force applied:
a = 13.5 m/s^2 (given)
m = 500 kg (mass of the car and rider)
Therefore, rearranging the formula, we have:
F = a * m
F = 13.5 m/s^2 * 500 kg
F = 6750 N
So, an extra force of 6750 Newtons was applied.
2. For the second problem, we can use the same formula, a = F/m, to find the acceleration:
a = F/m
F = 40 N (given)
m = 50 kg (mass of the cart)
Therefore, rearranging the formula, we have:
a = F/m
a = 40 N / 50 kg
a = 0.8 m/s^2
So, the acceleration of the cart is 0.8 m/s^2.
3. For the third problem, the weight of a person on the surface of the Earth can be calculated using the formula:
Weight = m * g
m = 80.2 kg (mass of the person)
g = 9.8 m/s^2 (acceleration due to gravity on Earth)
Therefore, using the formula, we have:
Weight = 80.2 kg * 9.8 m/s^2
Weight = 787.96 N
So, the weight of the person on the surface of the Earth is 787.96 Newtons.
4. For the fourth problem, we can use the same formula to find the acceleration of gravity on the Moon:
Weight = m * g
Weight = 94.0 N (given)
m = 75.0 kg (mass of the person)
Therefore, using the formula, we have:
g = Weight / m
g = 94.0 N / 75.0 kg
g = 1.253 m/s^2
So, the acceleration due to gravity on the Moon is approximately 1.253 m/s^2.
5. For the fifth problem, we can use the formula a = F/m to find the acceleration of Yuri Gagarin and the spacecraft:
a = F/m
F = 20.0 N (given)
m = 50.0 kg (mass of Yuri Gagarin), 85.0 kg (mass of the spacecraft)
a_Yuri = 20.0 N / 50.0 kg
a_Yuri = 0.4 m/s^2
a_spacecraft = 20.0 N / 85.0 kg
a_spacecraft = 0.235 m/s^2
The force exerted by Yuri Gagarin is greater than the force exerted by the spacecraft (20 N vs 20 N).
The acceleration of Yuri Gagarin is greater than the acceleration of the spacecraft (0.4 m/s^2 vs 0.235 m/s^2).
To solve the problems, we will use the formula:
a = F/m
1. A 500 kg car and rider accelerate at 13.5 m/s^2. How much extra force was applied?
Given:
m = 500 kg
a = 13.5 m/s^2
Using the formula: a = F/m, we can rearrange it to solve for F:
F = m * a
Substituting the values we have:
F = 500 kg * 13.5 m/s^2
F = 6750 N
The extra force applied to accelerate the car and rider is 6750 Newtons.
2. What is the acceleration of a 50 kg cart if the net force on it is 40 N?
Given:
m = 50 kg
F = 40 N
Using the formula: a = F/m
Substituting the values we have:
a = 40 N / 50 kg
a = 0.8 m/s^2
The acceleration of the 50 kg cart is 0.8 m/s^2.
3. What is the weight of an 80.2 kg person on the surface of the Earth?
Given:
m = 80.2 kg
g (acceleration due to gravity) = 9.8 m/s^2
Using the formula: a = F/m, we can rearrange it to solve for F:
F = m * g
Substituting the values we have:
F = 80.2 kg * 9.8 m/s^2
F ≈ 787.96 N
The weight of an 80.2 kg person on the surface of the Earth is approximately 787.96 Newtons.
4. A 75.0 kg person weighs 94.0 N on the Moon. What is the acceleration of gravity on the Moon?
Given:
m = 75.0 kg
F = 94.0 N
Using the formula: a = F/m
Substituting the values we have:
a = 94.0 N / 75.0 kg
a ≈ 1.2533 m/s^2
The acceleration of gravity on the Moon is approximately 1.2533 m/s^2.
5. 50.0 kg Yuri Gagarin is freely floating in space and pushes on a freely floating 85.0 kg spacecraft with a force of 20.0 N for 2 seconds.
To compare the forces exerted by Yuri Gagarin and the spacecraft, we can calculate the acceleration of both:
For Yuri Gagarin:
m = 50 kg
F = 20 N
t = 2 s
Using the formula: a = F/m
Substituting the values we have:
a = 20 N / 50 kg
a = 0.4 m/s^2
For the spacecraft:
m = 85 kg
F = 20 N (the force exerted by Yuri Gagarin)
t = 2 s
Using the formula: a = F/m
Substituting the values we have:
a = 20 N / 85 kg
a ≈ 0.235 m/s^2
The force exerted by Yuri Gagarin is the same on both him and the spacecraft, which is 20 N. However, the acceleration of Yuri Gagarin (0.4 m/s^2) is higher compared to that of the spacecraft (0.235 m/s^2).