The angle of the string with the vertical direction at the maximum height is 43.7°.
At the maximum height, the pendulum's kinetic energy will have been converted entirely into potential energy. Therefore, we can write the following equation:
(1/2)mv^2 = mgh
where
m is the mass of the pendulum (1.8 kg)
v is the initial speed of the pendulum (1.7 m/s)
h is the maximum height of the pendulum (what we are trying to find)
g is the acceleration due to gravity (9.81 m/s^2)
Solving for h, we get:
h = (v^2)/(2g)
Substituting the known values, we get:
h = (1.7 m/s)^2 / (2 × 9.81 m/s^2)
h = 0.147 m
Therefore, the maximum height of the pendulum is 0.147 m.
Angle of the string at the maximum height
At the maximum height, the pendulum will be at rest. Therefore, the tension in the string will be equal to the weight of the pendulum. This means that the angle of the string with the vertical direction will be given by:
cos(θ) = mg / T
where:
θ is the angle of the string with the vertical direction
T is the tension in the string
Substituting the known values, we get:
cos(θ) = (1.8 kg × 9.81 m/s^2) / (2.5 m × g)
cos(θ) = 0.72
θ = 43.7° .
Question
A point mass (1.8 kg) is suspended from the ceiling by a massless string. If the mass is given an initial speed of 1.7 m/s at the bottom, what maximum height does it achieve? (Assume its initial height represents h=0)(Give your answer to 3 sig figs.) 0.147 m Computer's answer now shown above. You are correct. Your receipt no. is 165-5106 Previous Tries At the maximum height, what angle does the string make with the vertical direction? Assume the string has a length of L =2.5 m. (Give your answer to 3 sig figs. and in the unit of deg) Submit Answer Incorrect. Tries 1/4 Previous Tries.