A 43 N toy is placed in a light swing that is attached to ropes 1.7 m long.
(a) Find the gravitational potential energy associated with the toy relative to its lowest position when the ropes are horizontal.
J
(b) Find the gravitational potential energy associated with the toy relative to its lowest position when the ropes make a 30° angle with the vertical.
J
A) PE of gravity= m*g*h
m=mass of object
g=acceleration due to gravity
h= distance
mass= weight/gravity=4.383
PE=(4.383kg)(9.81 m/s^2)(1.7m)
PE=73.095 J
To calculate the gravitational potential energy associated with the toy in different positions, we need to use the formula:
Gravitational Potential Energy = mass × gravitational acceleration × height
(a) When the ropes are horizontal, the height is equal to the length of the ropes, which is 1.7 m. The gravitational acceleration is approximately 9.8 m/s^2. The mass of the toy is not given, but we can use the weight (force due to gravity) to find the mass. The weight can be calculated using the formula:
Weight = mass × gravitational acceleration
In this case, the weight is given as 43 N. Rearranging the formula, we get:
mass = Weight / gravitational acceleration
mass = 43 N / 9.8 m/s^2
Now, we can calculate the gravitational potential energy:
Gravitational Potential Energy = mass × gravitational acceleration × height
Gravitational Potential Energy = (mass) × (9.8 m/s^2) × (1.7 m)
(b) When the ropes make a 30° angle with the vertical, the height is equal to the vertical component of the ropes' length. The vertical component can be found by multiplying the length of the ropes (1.7 m) by the sine of the angle (30°). So, the height is:
height = 1.7 m × sine(30°)
Now, we can calculate the gravitational potential energy:
Gravitational Potential Energy = mass × gravitational acceleration × height
Note: mass is the same as calculated in part (a).
Gravitational Potential Energy = (mass) × (9.8 m/s^2) × (height)
Gravitational Potential Energy = (mass) × (9.8 m/s^2) × (height)