A 7 kg block slides on a horizontal frictionless surface with a speed of 1.2 m/s. It is brought momentarily to rest when it hits a bumper that compresses a spring. The acceleration of gravity is 9.8 m/s^2.
To answer this question, we need to determine the characteristics of the bumper and the spring in order to calculate the force exerted on the block when it hits the bumper.
First, let's consider the initial speed of the block before it hits the bumper. The speed is given as 1.2 m/s.
Next, we need to determine the change in velocity as the block is brought to rest by the bumper. The final velocity is 0 m/s since the block comes to rest. The initial velocity is given as 1.2 m/s. Therefore, the change in velocity (Δv) is calculated as:
Δv = final velocity - initial velocity
Δv = 0 m/s - 1.2 m/s
Δv = -1.2 m/s
Now, we can determine the deceleration acting on the block by the bumper. This deceleration is denoted as "a." Using the equation for acceleration:
a = Δv / t
Here, we don't have the time (t) directly given in the question. However, we can solve for it using another relevant information - the gravitational acceleration (g).
The equation for the vertical motion (since the block hits a horizontal bumper) can be used to find the time it takes for the block to stop:
v = u + at
Since the block only experiences vertical motion due to gravity at this point, there is no initial vertical velocity (u = 0). Therefore, the equation simplifies to:
v = gt
Now, we can rearrange the equation to isolate time (t):
t = v / g
Plugging in the values, we have:
t = (-1.2 m/s) / (9.8 m/s^2) ≈ -0.1224 seconds
It is important to note that time cannot be negative, so the negative sign is ignored in this case. Thus, the time it takes for the block to stop is approximately 0.1224 seconds.
Next, we can calculate the deceleration (a) using the formula:
a = Δv / t
Plugging in the values:
a = (-1.2 m/s) / (0.1224 s)
a ≈ -9.8 m/s^2
The deceleration of the block when it hits the bumper is approximately -9.8 m/s^2.
Finally, let's determine the force exerted on the block by the bumper. Since the horizontal surface is frictionless, the only force acting on the block is due to the spring compression.
According to Newton's second law, the force (F) exerted on an object is equal to the mass (m) of the object multiplied by its acceleration (a):
F = m * a
Given: mass (m) = 7 kg, acceleration (a) = -9.8 m/s^2
F = (7 kg) * (-9.8 m/s^2)
F ≈ -68.6 N
Therefore, the force exerted on the block when it hits the bumper is approximately -68.6 Newtons.