A block of mass 6 kg, which has an initial
velocity of 4.1 m/s at time t = 0, slides on a
horizontal surface.
Calculate the work that must be done on
the block to bring it to rest.
Answer in units of J.
If a constant friction force of 7.1 Newtons is
exerted on the block by the surface, what is
the acceleration?
Answer in units of m/s
2
Determine the distance that the block slides
as it comes to rest.
Answer in units of m.
1. W = Change in KE = 0.5M*Vo^2 = 0.5*6*4.1^2 = 50.4 J.
Ff = M*a.
-7.1 = 6*a.
a = -1.18 m/s^2.
2. V^2 = Vo^2 + 2a*d = 0.
4.1^2 + (-2.36)d = 0,
d =
To find the work done on the block to bring it to rest, we need to use the work-energy principle. The work done on an object is equal to the change in its kinetic energy. In this case, the initial kinetic energy of the block is given by (1/2)mv^2, where m is the mass of the block and v is its initial velocity.
Initial kinetic energy = (1/2)(6 kg)(4.1 m/s)^2
To bring the block to rest, its final kinetic energy is 0. Therefore, the work done on the block is equal to the negative of its initial kinetic energy since the initial kinetic energy is being taken away.
Work done = - (1/2)(6 kg)(4.1 m/s)^2
Now we can calculate the numerical value:
Work done = - (1/2)(6)(4.1)^2 J
Next, to find the acceleration of the block while sliding, we can use Newton's second law of motion which states that the net force acting on an object is equal to its mass multiplied by its acceleration. In this case, the net force is the friction force exerted on the block by the surface.
Net force = mass × acceleration
The friction force is given as 7.1 Newtons, and the mass of the block is 6 kg.
7.1 N = 6 kg × acceleration
Solving for acceleration:
acceleration = 7.1 N / 6 kg
Finally, to determine the distance that the block slides as it comes to rest, we can use the equation of motion for constant acceleration, which relates distance, initial velocity, acceleration, and time:
distance = (initial velocity × time) + (1/2) × (acceleration × time^2)
Here, the initial velocity is 4.1 m/s. Since the block is coming to rest, we can assume the final velocity is 0. Also, note that we do not have the value of time. However, we can calculate it using the formula:
final velocity^2 = initial velocity^2 + 2 × acceleration × distance
where the final velocity is 0. Solving for distance:
distance = (final velocity^2 - initial velocity^2) / (2 × acceleration)
Substituting the given values:
distance = (0 - (4.1 m/s)^2) / (2 × acceleration)
Now, you can calculate the numerical value for the distance by substituting the value of acceleration we found earlier.
Please note that this is a step-by-step explanation of how to solve the problem mathematically.