Now let's focus on the descending sphere. let m be the mass of the sphere, g be the acceleration due to gravity, t be the magnitude of the force of tension of the string, a be the acceleration of the sphere as it descends, and α be the angular acceleration of the wheel. what is the correct expression for newton's second law applied to the descending sphere? a. mg+t = ma
b. mg+t = mα
c. mg-t = ma
d. mg-t = mα
e. -mg+t = ma
f. mg-tr = ma
g. mg+tr = ma

The position of a dragonfly that is flying parallel to the ground is given as a function of time by r⃗ =[2.90m+(0.0900m/s2)t2]i^− (0.0150m/s3)t3j^. a: at what value of t does the velocity vector of the insect make an angle of 34.0 degree clockwise from the x-axis? b: at the time calculated in part (a), what is the magnitude of the acceleration vector of the insect? c : at the time calculated in part (a), what is the direction of the acceleration vector of the insect?

You can decrease the resistance of a length of wire by

Agroup of monkeys is trying to cross the river in a rowboat. the maximum buoyant force on the rowboat is 2,000 n. the weight of the rowboat is 1,000 n. each monkey has a weight of 150 n. how many monkeys can safely cross in the rowboat at one time? explain your reasoning, including any calculations you used to find the answer.