A 0.33- kg pendulum bob is attached to a string 1.2 m long and hangs vertically as shown in Figure 1. What is the change in the pendulum bob’s gravitational potential energy as it swings from the lowest point of the pendulum to a point that is 35 degree to the vertical?
p=mgh
p=.33*9.8*(1.2-1.2*cos35)
P=70.2M
Are you sure ?
can you give the solution?
Draw the picture and do some geometry. 1.2m can be put on the other side of the triangle. The lower portion of the B ball we will call h. Cos(theta) = y / 1.2m ---> y = cos(theta) x 1.2m. (y is the length from the tip till the part what h is). Gotta do some algebra to get the acutal length of h, which I'm sure you can do yourself. You can then solve PE from there with the Potential Energy Formula. PE = mgh
To calculate the change in gravitational potential energy of the pendulum bob as it swings from the lowest point to an angle of 35 degrees to the vertical, we need to consider the equation for gravitational potential energy.
The gravitational potential energy (ΔPE) of an object depends on its mass (m), the acceleration due to gravity (g), and the change in height (Δh). The equation is:
ΔPE = m * g * Δh
In this case, the mass of the pendulum bob is given as 0.33 kg. The acceleration due to gravity can be assumed as 9.8 m/s^2.
To determine the change in height, we first need to find the vertical distance the bob travels from the lowest point to an angle of 35 degrees. This can be calculated using simple trigonometry.
The height change (Δh) can be found using the formula:
Δh = L * (1 - cos θ)
Where:
L = Length of the string (1.2 m in this case)
θ = Angle from the vertical (35 degrees in this case)
Substituting the values in the formula:
Δh = 1.2 * (1 - cos 35)
Using a calculator to find cos 35 ≈ 0.8192:
Δh = 1.2 * (1 - 0.8192) ≈ 0.2176 m
Now, we have all the required values to calculate the change in gravitational potential energy:
ΔPE = m * g * Δh
= 0.33 kg * 9.8 m/s^2 * 0.2176 m
≈ 0.68 Joules
Therefore, the change in the pendulum bob's gravitational potential energy as it swings from the lowest point to a point that is 35 degrees to the vertical is approximately 0.68 Joules.
Figure from the geometry the change in vertical height.
PE=mgh
Yes, I could.
I will be happy to check your work, but you need to do your own thinking. Answer grazers learn nothing.