A 2.0-kg brick is moving at a speed of 6.0m/s. How large a force F is needed to stop the brick in a time of 7.0x10^-4 s?
Force * time = change of momentum
T (7*10^-4) = 2 * 6
To find the force required to stop the brick in a given time, we can use the equation:
F = Δp / Δt
where F is the force, Δp is the change in momentum, and Δt is the change in time.
The momentum (p) of an object is defined as the product of its mass (m) and velocity (v):
p = m * v
Given:
Mass of the brick (m) = 2.0 kg
Initial velocity of the brick (v) = 6.0 m/s
Time interval (Δt) = 7.0 x 10^-4 s
First, let's calculate the initial momentum of the brick:
p_initial = m * v
p_initial = 2.0 kg * 6.0 m/s
p_initial = 12.0 kg·m/s
Next, let's calculate the final momentum of the brick. Since we want to stop the brick, the final velocity (v_final) is zero:
p_final = m * v_final
Since v_final = 0, the final momentum becomes:
p_final = m * 0
p_final = 0 kg·m/s
Now, let's calculate the change in momentum:
Δp = p_final - p_initial
Δp = 0 kg·m/s - 12.0 kg·m/s
Δp = -12.0 kg·m/s
Finally, let's calculate the force required to achieve this change in momentum in the given time:
F = Δp / Δt
F = (-12.0 kg·m/s) / (7.0 x 10^-4 s)
F = -1.71 x 10^4 N
Therefore, a force of approximately -1.71 x 10^4 N is needed to stop the brick in a time of 7.0 x 10^-4 s. The negative sign indicates that the force is in the opposite direction of the brick's initial velocity.