Pam has a mass of 35.5 kg and she is at rest on smooth, level, frictionless ice. Pam straps on a rocket pack. The rocket supplies a constant force for 29.2 m and Pam acquires a speed of 64.1 m/s.
What is the magnitude of the force?
V^2 = Vo^2 + 2a*d
V = 64.1 m/s
Vo = 0
d = 29.2 m.
Solve for a.
F = M*a
M = 35.5 kg
Solve for F.
To find the magnitude of the force supplied by the rocket pack, we can use Newton's second law of motion, which states that the force acting on an object is equal to the mass of the object multiplied by its acceleration.
In this scenario, Pam starts from rest (zero velocity) and reaches a final speed of 64.1 m/s. We can assume that the acceleration is constant, as the force supplied by the rocket pack is also constant.
First, we need to calculate the acceleration of Pam using the equation:
(v^2 - u^2) = 2as
Where:
v = Final velocity = 64.1 m/s
u = Initial velocity = 0 m/s (since Pam starts from rest)
a = Acceleration
s = Distance traveled = 29.2 m
Plugging in the values, we have:
(64.1^2 - 0^2) = 2a * 29.2
Simplifying:
(4112.81) = 58.4a
Dividing both sides by 58.4:
a ≈ 70.51 m/s^2
Now that we have the acceleration, we can find the magnitude of the force using Newton's second law:
Force (F) = mass (m) * acceleration (a)
Given:
mass (m) = 35.5 kg
acceleration (a) ≈ 70.51 m/s^2
Plugging in the values:
F = 35.5 kg * 70.51 m/s^2
Calculating:
F ≈ 2503.05 N
Therefore, the magnitude of the force supplied by the rocket pack is approximately 2503.05 Newtons.