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,
evaluate the resulting acceleration of the spacecraft.
To find the extra force applied in the first scenario, we use the formula:
a = F/m
Given:
m = 500 kg
a = 13.5 m/s^2
Substituting the values into the formula, we can rearrange to solve for F:
F = a * m
F = 13.5 m/s^2 * 500 kg
F = 6750 N
Therefore, an extra force of 6750 N was applied to the car and rider.
For the second scenario, to find the acceleration of a 50 kg cart with a net force of 40 N, we use the same formula:
a = F/m
Given:
m = 50 kg
F = 40 N
Substituting the values into the formula, we rearrange to solve for a:
a = F/m
a = 40 N / 50 kg
a = 0.8 m/s^2
Therefore, the acceleration of the cart is 0.8 m/s^2.
To find the weight of an 80.2 kg person on the surface of the Earth, we use the formula:
F = m * a
Given:
m = 80.2 kg
a = acceleration due to gravity = 9.8 m/s^2
Substituting the values into the formula, we can solve for F:
F = 80.2 kg * 9.8 m/s^2
F = 787.96 N
Therefore, the weight of the 80.2 kg person on the surface of the Earth is 787.96 N.
To find the acceleration of gravity on the Moon for the fourth scenario, we use the formula:
F = m * a
Given:
m = 75.0 kg
F = 94.0 N
Substituting the values into the formula, we can solve for a:
94.0 N = 75.0 kg * a
a = 94.0 N / 75.0 kg
a = 1.253 m/s^2
Therefore, the acceleration of gravity on the Moon is approximately 1.253 m/s^2.
For the fifth scenario, to compare the forces exerted by Yuri Gagarin and the spacecraft, we can calculate their respective accelerations:
a = F/m
Given:
For Yuri Gagarin: m = 50.0 kg, F = 20.0 N
For the spacecraft: m = 85.0 kg, F = 20.0 N
Substituting the values into the formula, we can calculate the respective accelerations:
For Yuri Gagarin:
a = 20.0 N / 50.0 kg
a = 0.4 m/s^2
For the spacecraft:
a = 20.0 N / 85.0 kg
a = 0.235 m/s^2
Comparing the forces, we see that both Yuri Gagarin and the spacecraft exert the same force, 20.0 N. However, the resulting accelerations are different, with Yuri Gagarin experiencing an acceleration of 0.4 m/s^2 and the spacecraft experiencing an acceleration of 0.235 m/s^2.
To answer your questions step-by-step, we'll use the formula a = F/m, where "a" is acceleration, "F" is force, and "m" is mass.
Question 1:
A 500 kg car and rider accelerate at 13.5 m/s^2. How much extra force was applied?
Step 1: Identify the given variables.
Mass (m) = 500 kg.
Acceleration (a) = 13.5 m/s^2.
Acceleration due to gravity (g) = 9.8 m/s^2.
Step 2: Rearrange the formula to solve for force.
F = m * a.
Step 3: Substitute the given values into the formula.
F = 500 kg * 13.5 m/s^2.
F = 6750 N.
Answer: The extra force applied is 6750 Newtons.
Question 2:
What is the acceleration of a 50kg cart if the net force on it is 40N?
Step 1: Identify the given variables.
Mass (m) = 50 kg.
Force (F) = 40 N.
Step 2: Rearrange the formula to solve for acceleration.
F = m * a.
Step 3: Rearrange the formula to solve for acceleration.
a = F / m.
Step 4: Substitute the given values into the formula.
a = 40 N / 50 kg.
a = 0.8 m/s^2.
Answer: The acceleration of the 50 kg cart is 0.8 m/s^2.
Question 3:
What is the weight of an 80.2 kg person on the surface of the Earth?
Step 1: Identify the given variables.
Mass (m) = 80.2 kg.
Acceleration due to gravity (g) = 9.8 m/s^2.
Step 2: Multiply the mass by the acceleration due to gravity.
Weight = m * g.
Weight = 80.2 kg * 9.8 m/s^2.
Answer: The weight of the 80.2 kg person on the surface of the Earth is 787.96 N.
Question 4:
A 75.0 kg person weighs 94.0 N on the Moon. What is the acceleration of gravity on the Moon?
Step 1: Identify the given variables.
Mass (m) = 75.0 kg.
Weight = 94.0 N.
Step 2: Set the weight equal to the product of mass and acceleration due to gravity.
Weight = m * g.
Step 3: Rearrange the formula to solve for acceleration due to gravity.
g = Weight / m.
Step 4: Substitute the given values into the formula.
g = 94.0 N / 75.0 kg.
Answer: The acceleration of gravity on the Moon is 1.2533 m/s^2.
Question 5:
Compare the forces exerted by Yuri Gagarin and the spacecraft.
Step 1: Identify the given variables.
Mass of Yuri Gagarin (m1) = 50.0 kg.
Mass of the spacecraft (m2) = 85.0 kg.
Force exerted by Yuri Gagarin (F1) = 20.0 N.
Time (t) = 2 seconds.
Step 2: Calculate the acceleration of the spacecraft using the formula a = F/m.
Acceleration of the spacecraft (a2) = F2 / m2.
Acceleration of the spacecraft (a2) = 20.0 N / 85.0 kg.
Acceleration of the spacecraft (a2) = 0.2353 m/s^2.
Step 3: Calculate the change in velocity of the spacecraft using the formula v = a * t.
Change in velocity of the spacecraft (Δv2) = a2 * t.
Change in velocity of the spacecraft (Δv2) = 0.2353 m/s^2 * 2 s.
Change in velocity of the spacecraft (Δv2) = 0.4706 m/s.
Step 4: Use the principle of conservation of momentum to calculate the force exerted by the spacecraft on Yuri Gagarin.
Force exerted by the spacecraft on Yuri Gagarin (F12) = (m1 * Δv2) / t.
Force exerted by the spacecraft on Yuri Gagarin (F12) = (50.0 kg * 0.4706 m/s) / 2 s.
Force exerted by the spacecraft on Yuri Gagarin (F12) = 11.765 N.
Answer: Yuri Gagarin exerts a force of 20.0 N on the spacecraft, while the spacecraft exerts a force of 11.765 N on Yuri Gagarin.