A  5.5-kg object moving with an initial velocity of 5.2 m/s comes to rest due to friction after it travels a horizontal distance of 10.2 m.If the initial speed of the object is doubled, what distance will it travel before coming to rest? Express your answer in meters, to at least one digit after the decimal point.

To solve this problem, we can use the concept of work done by friction. The work done by friction is equal to the change in kinetic energy of the object.

Given: Mass of the object (m) = 5.5 kg Initial velocity (v) = 5.2 m/s Distance traveled (d) = 10.2 m

First, let's calculate the initial kinetic energy (KE) of the object using the formula: KE = (1/2) * m * v^2

Substituting the given values: KE = (1/2) * 5.5 kg * (5.2 m/s)^2 KE = 71.68 J

Since the object comes to rest, the final kinetic energy is zero. Therefore, the work done by friction is equal to the initial kinetic energy.

Now, let's calculate the work done by friction (W) using the formula: W = KE

Substituting the value of KE: W = 71.68 J

Now, let's consider the case where the initial speed of the object is doubled. The new initial velocity (v') will be 2 times the initial velocity (v).

v' = 2 * v v' = 2 * 5.2 m/s v' = 10.4 m/s

Using the same formula as before, let's calculate the new initial kinetic energy (KE'):

KE' = (1/2) * m * (v')^2 KE' = (1/2) * 5.5 kg * (10.4 m/s)^2 KE' = 286.72 J

Since the object comes to rest, the final kinetic energy is zero. Therefore, the work done by friction is equal to the initial kinetic energy.

W' = KE' W' = 286.72 J

Now, let's find the distance traveled (d') when the object comes to rest with the new initial velocity.

Using the formula for work done by friction: W' = force of friction * d'

Since the force of friction is constant, we can equate the work done by friction in both cases:

W = W' force of friction * d = force of friction * d'

Simplifying the equation: d' = (W / force of friction) * d

Substituting the values: d' = (71.68 J / force of friction) * 10.2 m

To find the distance traveled before coming to rest with the new initial velocity, we need to find the force of friction. The force of friction can be calculated using the formula:

force of friction = coefficient of friction * normal force

Since the object is moving horizontally, the normal force is equal to the weight of the object, which can be calculated using the formula:

weight = mass * acceleration due to gravity

Substituting the values: weight = 5.5 kg * 9.8 m/s^2 weight = 53.9 N

Now, let's find the coefficient of friction. The coefficient of friction can be calculated using the formula:

coefficient of friction = force of friction / normal force

Substituting the values: coefficient of friction = force of friction / 53.9 N

Now, we can substitute the value of the coefficient of friction into the equation for d':

d' = (71.68 J / (coefficient of friction * 53.9 N)) * 10.2 m

Calculating the value of d' will give us the distance traveled before coming to rest with the new initial velocity.

To solve this problem, we can use the concept of work done by friction. The work done by friction is equal to the change in kinetic energy of the object.

Given: Mass of the object (m) = 5.5 kg Initial velocity (v) = 5.2 m/s Distance traveled (d) = 10.2 m

First, let's calculate the initial kinetic energy (KE) of the object using the formula: KE = (1/2) * m * v^2

Substituting the given values: KE = (1/2) * 5.5 kg * (5.2 m/s)^2 KE = 71.68 J

Since the object comes to rest, the final kinetic energy is zero. Therefore, the work done by friction is equal to the initial kinetic energy.

Now, let's calculate the work done by friction (W) using the formula: W = KE

Substituting the value of KE: W = 71.68 J

Now, let's consider the case where the initial speed of the object is doubled. The new initial velocity (v') will be 2 times the initial velocity (v).

v' = 2 * v v' = 2 * 5.2 m/s v' = 10.4 m/s

Using the same formula as before, let's calculate the new initial kinetic energy (KE'):

KE' = (1/2) * m * (v')^2 KE' = (1/2) * 5.5 kg * (10.4 m/s)^2 KE' = 286.72 J

Since the object comes to rest, the final kinetic energy is zero. Therefore, the work done by friction is equal to the initial kinetic energy.

W' = KE' W' = 286.72 J

Now, let's find the distance traveled (d') when the object comes to rest with the new initial velocity.

Using the formula for work done by friction: W' = force of friction * d'

Since the force of friction is constant, we can equate the work done by friction in both cases:

W = W' force of friction * d = force of friction * d' d' = (W / force of friction)

Substituting the values of W and force of friction (which is the same in both cases):

d' = (71.68 J) / force of friction

Now, we need to find the force of friction. The force of friction can be calculated using the formula:

force of friction = coefficient of friction * normal force

Since the object is moving horizontally, the normal force is equal to the weight of the object, which can be calculated using the formula:

weight = mass * acceleration due to gravity

weight = 5.5 kg * 9.8 m/s^2 weight = 53.9 N

Now, let's find the coefficient of friction. The coefficient of friction can be calculated using the formula:

coefficient of friction = force of friction / normal force

Substituting the values:

coefficient of friction = force of friction / 53.9 N

Now, we can substitute the value of the coefficient of friction into the equation for d':

d' = (71.68 J) / (coefficient of friction * 53.9 N)

Calculating the value of d':

d' = (71.68 J) / (coefficient of friction * 53.9 N)

Finally, we can calculate the distance traveled (d'):

d' = (71.68 J) / (coefficient of friction * 53.9 N)

Please note that the specific value of the coefficient of friction is not given in the question, so we cannot provide an exact numerical answer.