A pendulum of length L=26.0 cm and mass m= 168 g is released from rest when the cord makes an angle of 65.2 degrees with the vertical.

A) how far (m) does the mass fall before reaching its lowest point?

My work: .26m - .109 = .151 m

B) how much work (J) is done by gravity as it falls to its lowest point?

My work: (.168 kg)(9.8 m/s)= 1.646 N
.26cos65.2 = .109

C) how much work (J) is done by the string tension as it falls to its lowest point?

My work: same as b

A) To find how far the mass falls before reaching its lowest point, you can use trigonometry. Given that the length of the pendulum is L = 26.0 cm, and the angle made by the cord with the vertical is 65.2 degrees, you can use the cosine function.

The distance the mass falls before reaching the lowest point (d) can be calculated as:
d = L - L * cos(theta)

Substituting the given values:
d = 26.0 cm - 26.0 cm * cos(65.2 degrees)

Converting the units to meters:
d = 0.26 m - 0.26 m * cos(65.2 degrees)

Evaluating the cosine function:
d ≈ 0.26 m - 0.26 m * 0.4226

Calculating the final result:
d ≈ 0.26 m - 0.109 m
d ≈ 0.151 m

Therefore, the mass falls approximately 0.151 meters before reaching its lowest point.

B) To find the work done by gravity as the mass falls to its lowest point, you can use the formula for gravitational potential energy. The work done by gravity is equal to the change in potential energy.

The potential energy change (ΔPE) can be calculated as:
ΔPE = m * g * h

Given that the mass of the pendulum is m = 168 g (0.168 kg) and the acceleration due to gravity is g = 9.8 m/s², you need to find the difference in height (h).

Since the pendulum is released from rest, the potential energy at the highest point is zero, and at the lowest point, it is equal to m * g * h.

Substituting the values:
ΔPE = (0.168 kg) * (9.8 m/s²) * (0.151 m)

Calculating the final result:
ΔPE ≈ 0.254 J

Therefore, the work done by gravity as the mass falls to its lowest point is approximately 0.254 Joules.

C) The work done by the string tension can be calculated similarly to the work done by gravity. Since the tension force is perpendicular to the displacement, the work done by the string tension is zero. Therefore, no work is done by the string tension as the mass falls to its lowest point.

A) To find how far the mass falls before reaching its lowest point, you can use trigonometry. The length of the pendulum, L, is given as 26.0 cm. When the cord makes an angle of 65.2 degrees with the vertical, the horizontal distance the mass falls can be found using cosine function:

Distance fallen = L * cos(angle)
Distance fallen = 26.0 cm * cos(65.2 degrees)

You can use a calculator to calculate the value of cos(65.2 degrees) and then multiply it by the given length L to get the distance fallen in meters.

B) To find the work done by gravity as the mass falls to its lowest point, you need to consider the gravitational potential energy. The work done by gravity is equal to the change in gravitational potential energy. The gravitational potential energy is given by the formula:

Gravitational potential energy = mass * acceleration due to gravity * height

In this case, the height is the distance fallen that you calculated in part A. The mass is given as 168 g, so you need to convert it to kilograms by dividing by 1000.

Work done by gravity = mass * acceleration due to gravity * distance fallen

You can substitute the values into the equation and calculate the work done.

C) The work done by the tension in the string can be calculated by considering the tension force and the distance over which it acts. As the mass falls, the tension in the string does positive work to counteract gravity and keep the mass in motion. The work done by the string tension is given by the formula:

Work done by tension = tension force * distance fallen

The tension force can be found using Newton's second law, which states that the net force acting on an object is equal to the mass times the acceleration. In this case, the net force is the tension force, and the acceleration is the centripetal acceleration.

Centripetal acceleration = (velocity^2) / radius

The velocity can be calculated using the conservation of energy principle. At the lowest point of the swing, all the gravitational potential energy is converted to kinetic energy. So, you can equate the gravitational potential energy at the highest point (when the pendulum is released) with the kinetic energy at the lowest point (when it reaches its lowest point).

Gravitational potential energy at highest point = Kinetic energy at lowest point

Mass * acceleration due to gravity * height = (1/2) * mass * velocity^2

Solve for the velocity and substitute it back into the equation for centripetal acceleration. Then calculate the tension force using Newton's second law. Finally, multiply the tension force by the distance fallen to find the work done by the string tension.