A lump of clay with a mass of 5.0 ! 10-2 kg is thrown toward a wall with a velocity of 3.0 m/s. The
clay bounces off the wall with a velocity of #0.5 m/s. What is the impulse on the clay?
If the clay in the previous problem impacted the wall for 5.0 ms, what was the average force on the
clay?
Why did the lump of clay get all the attention at the art gallery? Because it had great "impulse"!
But let's get serious for a moment. To find the impulse on the clay, we can use the formula:
Impulse = change in momentum
The momentum of an object is given by the product of its mass and velocity. In this case, the clay's mass is given as 5.0 × 10^-2 kg, and its initial velocity is 3.0 m/s. After bouncing off the wall, its velocity changes to -0.5 m/s (assuming the negative sign indicates direction).
So, the change in momentum is given by:
Change in momentum = (final momentum) - (initial momentum)
Let's calculate the initial momentum first:
Initial momentum = (mass) × (initial velocity)
Initial momentum = (5.0 × 10^-2 kg) × (3.0 m/s)
Initial momentum = 0.15 kg m/s
Now, let's calculate the final momentum:
Final momentum = (mass) × (final velocity)
Final momentum = (5.0 × 10^-2 kg) × (-0.5 m/s) [Note: The velocity is negative because the direction of motion is reversed]
Final momentum = -0.025 kg m/s
Now we can find the change in momentum:
Change in momentum = (-0.025 kg m/s) - (0.15 kg m/s)
Change in momentum = -0.175 kg m/s
Finally, we can determine the impulse by taking the absolute value of the change in momentum (since impulse is a scalar quantity):
Impulse = |change in momentum|
Impulse = |-0.175 kg m/s|
Impulse = 0.175 kg m/s
Now let's move on to the next question, shall we?
To find the impulse on the clay, we can use the equation:
Impulse = Change in momentum
The momentum of an object is given by the equation:
Momentum = Mass x Velocity
Given:
Mass of the clay = 5.0 x 10^-2 kg
Initial velocity of the clay = 3.0 m/s
Final velocity of the clay = -0.5 m/s (since it bounces off the wall)
First, let's calculate the initial momentum of the clay:
Initial momentum = Mass x Initial velocity
= (5.0 x 10^-2 kg) x (3.0 m/s)
= 0.15 kg·m/s
Next, let's calculate the final momentum of the clay:
Final momentum = Mass x Final velocity
= (5.0 x 10^-2 kg) x (-0.5 m/s)
= -0.025 kg·m/s
Now, we can calculate the change in momentum:
Change in momentum = Final momentum - Initial momentum
= (-0.025 kg·m/s) - (0.15 kg·m/s)
= -0.175 kg·m/s
Therefore, the impulse on the clay is -0.175 kg·m/s.
To find the average force on the clay, we can use the equation:
Average force = Impulse / Time
Given:
Time of impact = 5.0 ms = 5.0 x 10^-3 s
Now, let's calculate the average force:
Average force = (-0.175 kg·m/s) / (5.0 x 10^-3 s)
= -35 N
Therefore, the average force on the clay is -35 Newtons. Note that the negative sign indicates that the force is in the opposite direction of the initial velocity of the clay.
To find the impulse on the clay, we can use the equation:
Impulse = Change in momentum
The momentum of an object is given by the product of its mass and velocity:
Momentum = mass * velocity
The change in momentum is the difference between the final momentum and the initial momentum. In this case, the initial momentum is the product of the mass (5.0 * 10^(-2) kg) and the initial velocity (3.0 m/s), while the final momentum is the product of the mass (5.0 * 10^(-2) kg) and the final velocity (-0.5 m/s) because the clay is bouncing back in the opposite direction.
Therefore, the change in momentum is:
Change in momentum = (mass * final velocity) - (mass * initial velocity)
Substituting the values, we get:
Change in momentum = (0.05 kg * -0.5 m/s) - (0.05 kg * 3.0 m/s)
Simplifying, we have:
Change in momentum = (-0.025 kg·m/s) - (0.15 kg·m/s)
Change in momentum = -0.175 kg·m/s
So, the impulse on the clay is -0.175 kg·m/s.
Now, to find the average force exerted on the clay, we can use the equation:
Average force = Impulse / Time
Given that the time the clay impacted the wall is 5.0 ms, we need to convert it to seconds:
Time = 5.0 ms = 5.0 * 10^(-3) s
Substituting the values, we get:
Average force = -0.175 kg·m/s / 5.0 * 10^(-3) s
Simplifying, we have:
Average force = -35 N
Therefore, the average force on the clay is -35 Newtons. Note that the negative sign indicates that the force is acting in the opposite direction of motion.
Impulse equals momentum change
= 3.5 m/s*5*10^-2 kg = 0.175 kg m/s
Divide that by 0.005 s for the average force, in newtons.