Question

During a Physics demonstration, Mr. Atwood lifts a 5.93-kg object vertically a distance of 2.09 meters using a light string. The tension in the string is 82.0 Newtons. Determine the final speed of the object if it starts from rest.

Answer 1

To find the final speed of the object, apply Newton's second law to calculate the acceleration and then use kinematic equations to compute the final velocity after moving a certain distance.

Step-by-step explanation:

The problem involves calculating the final speed of a 5.93-kg object that has been lifted vertically using a string with a tension of 82.0 Newtons, starting from rest. Using Newton's second law and kinematic equations, we can determine the acceleration and use it to find the final speed after moving 2.09 meters. It requires applying the formula T = mg + ma and v^2 = u^2 + 2as, where T is the tension in the string, m is the mass, g is the acceleration due to gravity, a is the acceleration, v is the final velocity, u is the initial velocity, and s is the distance.

First, find the acceleration (a) using the equation:

T = mg + ma

82.0 N = (5.93 kg)(9.80 m/s2) + (5.93 kg)a

Solve for a to find the acceleration. Then use the acceleration in the kinematic equation:

v2 = u2 + 2as

With u being zero (since it starts from rest), and substituting the value of a and s (2.09 m), we can calculate the final speed v.

Answer 2

The final speed of a 5.93-kg object lifted vertically 2.09 meters with a tension force of 82.0 N can be found using the work-energy principle, resulting in approximately 7.62 m/s.

Step-by-step explanation:

The student asks about determining the final speed of an object lifted by a light string with a given tension, starting from rest. Using the work-energy principle, the work done by the tension force is equal to the change in kinetic energy. Since the object starts from rest, its initial kinetic energy is zero. The work done by the tension can be calculated as the tension force times the distance moved in the direction of the force.

Work done by tension (W) = tension (T) x distance (d)

W = 82.0 N x 2.09 m = 171.38 J (since the direction of force and displacement are the same)

Now, we relate this work to the change in kinetic energy (ΔKE):

ΔKE = Work done by tension (W) = 171.38 J

Since the initial kinetic energy is 0 (object starting from rest), the final kinetic energy KE_final is equal to the work done:

KE_final = 1/2 m v^2

171.38 J = 1/2 x 5.93 kg x v^2

Solving for v (final speed):

v = √(2 x 171.38 J / 5.93 kg)

v ≈ √(57.96 m^2/s^2)

v ≈ 7.62 m/s

The final speed of the object is approximately 7.62 m/s.