Having landed on a newly discovered planet, an astronaut sets up a simple pendulum of length 1.31 m and finds that it makes 247 complete oscillations in 793 s. The amplitude of the oscillations is very small compared to the pendulum’s length. What is the gravitational acceleration on the surface of this planet?

Aquantity of gas has a volume of 1.5 m3 and an absolute pressure of 95 kpa. when the gas is compressed to a volume of 0.5 m3, what is the new absolute pressure of the gas? (assume that there’s no change in temperature.)

Frank just graduated from eighth grade. assuming exactly four years from now he will graduate from high school how many seconds does he have until his high school graduation

Amass m = 74 kg slides on a frictionless track that has a drop, followed by a loop-the-loop with radius r = 18.4 m and finally a flat straight section at the same height as the center of the loop (18.4 m off the ground). since the mass would not make it around the loop if released from the height of the top of the loop (do you know why? ) it must be released above the top of the loop-the-loop height. (assume the mass never leaves the smooth track at any point on its path.) 1. what is the minimum speed the block must have at the top of the loop to make it around the loop-the-loop without leaving the track? 2. what height above the ground must the mass begin to make it around the loop-the-loop? 3. if the mass has just enough speed to make it around the loop without leaving the track, what will its speed be at the bottom of the loop? 4. if the mass has just enough speed to make it around the loop without leaving the track, what is its speed at the final flat level (18.4 m off the ground)? 5. now a spring with spring constant k = 15600 n/m is used on the final flat surface to stop the mass. how far does the spring compress?