Question

What force (in newtons) is required to accelerate a body with a mass of 32 kilograms at a rate of 12 m/s2? If a body with a mass of 4 kg is moved by a force of 20 N, what is the rate of its acceleration? A car with a mass of 1,500 kg is traveling at a speed of 30 m/s. What force must be applied to stop the car in 3 seconds? If a suitcase has a mass of 20 kg, what is the force of gravity acting on it? On the moon, what would be the force of gravity acting on an object that has a mass of 7 kg? On earth, what is a child’s mass if the force of gravity on the child’s body is 100 N?

Answer 1

Answer: 1. F = ma

F = 32 kg × 12 m/s2

F = 384 N

2. a=Fm

a

=

F

m

a=20 N4 kg

a

=

20

N

4

kg

a = 5 m/s2

3. Keep in mind that when the car stops, the final velocity is zero. Use the formula for final velocity to calculate the acceleration.

v2 = v1 + at

0 m/s = 30 m/s + (a × 3 s)

0 = 30 + 3a

Subtract 3a from both sides of the equation.

0 − 3a = 30 + 3a − 3a

−3a = 30

Divide both sides of the equation by –3 to solve for a.

a = –10 m/s

The acceleration is negative, which means that the car is slowing down. The force needed to cause such acceleration can be calculated as follows:

F = ma

F = 1,500 kg × (–10 m/s2)

F = –15,000 N

A deceleration or braking force of –15,000 N must be applied to stop the car in 3 seconds.

4. F = mg

F = 20 kg × 9.8 m/s2

F = 196 N

5. F=mg6

F

=

m

g

6

F=7 kg×9.8 m/s26

F

=

7

kg

×

9.8

m/s

2

6

F=68.66

F

=

68.6

6

F = 11.43 N

6. m=Fg

m

=

F

g

m=100 N9.8 m/s2

m

=

100

N

9.8

m/s

2

m = 10.2 kg

Explanation: Pen foster

Answer 2

One by one.

1) What force (in newtons) is required to accelerate a body with a mass of 32 kilograms at a rate of 12 m/s2?

Data:

m = 32 kg
a = 12 m/s^2

Principle / formula: Secon Law of Newton, F = m*a

=> F = 32 kg * 12 m/s^2 = 384 N

2) If a body with a mass of 4 kg is moved by a force of 20 N, what is the rate of its acceleration?

Data:

m = 4 kg
F = 20 N
a =?

Formula: F = m*a => a = F/m = 20N / 4kg = 5 m/s^2

3) A car with a mass of 1,500 kg is traveling at a speed of 30 m/s. What force must be applied to stop the car in 3 seconds?

Data:

m = 1500 kg
Vo = 30 m/s
Vf =?
t = 3 seconds
F = ?

Formulas:

F = m*a

a = [Vf - Vo]/t

=> a = [30m/s - 0] / 3 s = 30m/s / 3s = 10 m/s^2

=> F = 1500 kg * 10 m/s^2 = 15,000 N

4) If a suitcase has a mass of 20 kg, what is the force of gravity acting on it?

F = m * g = 20 kg * 9.8 m/s^2 = 196 N

5) On the moon, what would be the force of gravity acting on an object that has a mass of 7 kg?

Use g in the moon 1.625 m/s^2

F = m * g = 7 kg * 1.625 m/s^2 = 11.735 N

6) On earth, what is a child’s mass if the force of gravity on the child’s body is 100 N?

F = m * g => m = F / g = 100N / 9.8 m/s^2 = 10.2 kg