Do a mouse, a mouse pup, and 180 g of cheese hang together if the mouse is 100 g heavier? - briefly
Yes, the three items can be combined; the total mass equals the mouse’s weight plus the pup’s weight plus 180 g of cheese, which simplifies to 2 × (pup weight) + 280 g. This satisfies the condition that the mouse is 100 g heavier than the pup.
Do a mouse, a mouse pup, and 180 g of cheese hang together if the mouse is 100 g heavier? - in detail
The situation involves three objects suspended from a single support: an adult mouse, its offspring, and a piece of cheese weighing 180 g. The adult’s mass exceeds that of the juvenile by 100 g. To determine whether the three can remain together in static equilibrium, the total downward force must be compared with the maximum tensile capacity of the supporting element.
Assume the juvenile’s mass is m (grams). Then the adult’s mass equals m + 100 g. The combined mass is
- m (juvenile)
- m + 100 g (adult)
- 180 g (cheese)
Total mass = 2 m + 280 g. Converting to kilograms (divide by 1000) gives
(M = \frac{2m + 280}{1000}) kg.
The gravitational force acting on the system is
(F_g = M \times g = \frac{2m + 280}{1000} \times 9.81) N.
If the support can sustain a tension greater than or equal to (F_g), the three items will hang together without motion. For example, if the support’s rating is 5 N, the inequality
(\frac{2m + 280}{1000} \times 9.81 \le 5)
leads to
(2m + 280 \le \frac{5 \times 1000}{9.81} \approx 509.68) g,
so
(m \le \frac{509.68 - 280}{2} \approx 114.84) g.
Thus, provided the juvenile mouse weighs no more than about 115 g, the total load remains within a 5‑N capacity and the ensemble stays suspended.
If the support’s rating is higher, the permissible juvenile mass increases proportionally. The analysis applies to any tensile limit: calculate the total weight, compare with the limit, and solve for the unknown juvenile mass.
In summary, the three objects can hang together if the combined weight does not exceed the support’s tensile rating; this condition translates into a specific maximum mass for the younger mouse, derived from the given 100 g mass difference and the fixed cheese weight.